View source for RICE, PARIS and MERKLE – J-Integral Estimation Method

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<span style="font-size:1.2em;font-weight:bold;">J-integral estimation method according to RICE, PARIS and MERKLE (RPM)</span>
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==Basic assumption of the estimation method==

[[J-Integral Evaluation Method (Overview) | ''J''-integral estimation methods]] are used to determine fracture-mechanical [[Material Value | characteristic values]] according to the [[J-Integral Concept | ''J''-integral concept]].

The proposal for the determination of ''J''<sup>RPM</sup> values according to RICE, PARIS and MERKLE [1] is based on the consideration of the deformation of the unnotched specimen and represents a one-sample approximation method which is applicable for deeply notched [[Specimen | specimens]] with ''a''/''W'' > 0.6.


[[file:EvauationMethod_RPM1.jpg]]
{| 
|- valign="top"
|width="50px"|'''Fig. 1''': 
|width="600px" |Determination of load–loadpoint displacement diagrams for the calculation of ''J''<sub>I</sub><sup>RPM</sup> (''J''<sub>Ic</sub><sup>RPM</sup>, ''J''<sub>Id</sub><sup>RPM</sup>) [1, 2]
|}

==Determination equation for SENB an CT specimen==

The equation of determination is as follows:

{|
|-
|width="20px"|
|width="500px" | <math> J_{I}^{RPM}=\frac{\lambda_{1}}{B(W-a)}\int_{f_{0}}^{f_{max}}Fdf_{max}=\frac{\lambda_{1}(A_{G}-A_{0})}{B(W-a)}</math>
|}

For the [[SENB-Specimen | three-point bending test specimen (SENB)]], the following specification applies to ''&lambda;''<sub>1</sub>:

''&lambda;''<sub>1</sub> = 2 für ''a''/''W'' > 0.6

In the case of the [[Compact Tension (CT) Specimen]], the following relationship is used:

{|
|-
|width="20px"|
|width="500px" | <math> \lambda_{1}=f(a|W)\frac{1+\alpha}{1+\alpha^2}\ mit\ \alpha=\left [ \left [ (\frac{2a}{W-a})^2+2(\frac{2}{W-a})+2 \right ]^\frac{1}{2}-(\frac{2a}{W-a}) \right ]</math>
|}

''A''<sub>0</sub> can be determined experimentally from the deformation of the unnotched test specimen or also calculated (see [3]).


==Evaluation procedure==

The experimental procedure for determining geometry-independent fracture-mechanical characteristic values with the aid of the [[Instrumented Charpy Impact Test | instrumented Charpy impact test (ICIT)]] under dynamic loading is explained in detail in the validated procedure of the testing laboratory "Mechanical Testing of Plastics": [http://wiki.polymerservice-merseburg.de/index.php/MPK-Prozedur_MPK-IKBV_englisch MPK procedure "MPK-ICIT"] [4].

==See also==

*[[J-Integral Concept | J-integral concept]]
*[[J-Integral Evaluation Method (Overview) | J-Integral evaluation method (overview)]]
*J-integral estimation methods of
::- [[BEGLEY and LANDES – J-Integral Estimation Method | BEGLEY and LANDES]]
::- [[SUMPTER and TURNER – J-Integral Estimation Method | SUMPTER and TURNER]]
::- [[MERKLE and CORTEN – J-Integral Estimation Method | MERKLE and CORTEN (MC)]]
::- [[KANAZAWA – J-Integral Estimation Method | KANAZAWA]]


'''References'''

{|
|-valign="top"
|[1]
|Rice, J. R., Paris, J. G., Merkle, J. G.: Some Further Results of J-Integral Analysis and Estimates. In: Progress in Flaw Growth and Fracture Toughness Testing. ASTM STP 536 (1973) 231–245 (https://doi.org/10.1520/STP49643S)
|-valign="top"
|[2]
|[[Blumenauer, Horst|Blumenauer, H.]], Pusch, G.: Technische Bruchmechanik. Deutscher Verlag für Grundstoffindustrie, Leipzig Stuttgart (1993) 3. Edition (ISBN 3-342-00659-5; see [[AMK-Büchersammlung | AMK-Library]] under E 29-3)
|-valign="top"
|[3]
|[[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3. Edition, p. 246 and 251–253, (ISBN 978-1-56990-806-8; e-book 978-1-56990-807-5; see [[AMK-Büchersammlung | AMK-Library]] under A 22))
|-valign="top"
|[4]
|[http://wiki.polymerservice-merseburg.de/index.php/MPK-Prozedur_MPK-IKBV_englisch  MPK procedure "MPK-ICIT"] (2016-03): Testing of Plastics – Instrumented Charpy Impact Test (ICIT): Procedure for Determining the Crack Resistance Behaviour Using the Instrumented Impact Test; 

*Part I: Determination of Characteristic Fracture Mechanics Parameters for Resistance Against Unstable Crack Propagation;
*Part II: Determination of Characteristic Fracture Mechanics Parameters for Resistance Against Stable Crack Propagation

[[Category:Fracture Mechanics]]
[[Category:Instrumented Impact Test]]